LONDON—Opening arguments in a closely watched criminal trial involving former News Corp editors in the U.K. kicked off Wednesday with British prosecutors saying three former journalists at the company and a private investigator had already pleaded guilty to illegal mobile-phone voice-mail interception, or phone hacking.

The disclosure—the first public confirmation of these guilty pleas—represented the opening salvos by prosecutors as they began laying out their case against former News Corp executives Rebekah Brooks,...